Question

(x+9) ^2+(x-11)^2=2x^2

Answer 1

=x²+18x+81+x²-22x+121=2x²
2x²-4x+204=2x² 
4x=202 |÷4
x=50,5
Ответ: x=50,5.

Answer 2

To solve the equation $(x+9)^2 + (x-11)^2 = 2x^2$, you can start by expanding the squared terms and simplifying the equation:

$(x+9)^2 + (x-11)^2 = 2x^2$

Expanding the squared terms:

$x^2 + 18x + 81 + x^2 - 22x + 121 = 2x^2$

Now, combine like terms on the left side of the equation:

$2x^2 - 4x^2 + 18x - 22x + 81 + 121 = 0$

Simplify the equation:

$-2x^2 - 4x + 202 = 0$

Now, let's solve this quadratic equation for x. We can divide the entire equation by -2 to make it more manageable:

$x^2 + 2x - 101 = 0$

You can use the quadratic formula to solve for x, where $a = 1$, $b = 2$, and $c = -101$:

The quadratic formula is:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this case, $a = 1$, $b = 2$, and (c = -101, so:

$x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-101)}}{2(1)}$

Simplify:

$x = \frac{-2 \pm \sqrt{4 + 404}}{2}$

$x = \frac{-2 \pm \sqrt{408}}{2}$

Now, simplify the square root:

$x = \frac{-2 \pm 2\sqrt{102}}{2}$

You can simplify this further by factoring out a 2 in the numerator:

$x = \frac{2(-1 \pm \sqrt{102})}{2}$

Finally, you can cancel out the 2 in the numerator and denominator:

$x = -1 \pm \sqrt{102}$

So, the solutions for the equation $(x+9)^2 + (x-11)^2 = 2x^2$ are:

$x = -1 + \sqrt{102}$

and

$x = -1 - \sqrt{102}$